The International Olympic Committee revealed today that an agreement had been reached "in principle" for London organisers to avoid the need to build a temporary £42m arena by moving two sports to Wembley Arena.

Although the two sports involved – badminton and rhythmic gymnastics – have not yet officially approved the move, the chairman of the IOC co-ordination commission, Denis Oswald, said he was confident they would do so.

The Badminton World Federation's council is due to meet in Bali tomorrow to discuss the issue, while the International Gymnastics Federation has told the Guardian its executive board would not formally consider it until next year.

"There is some saving to make – the two federations have been very co-operative and understand it was wise to look for a cheaper solution," said Oswald, chairman of the IOC body responsible for regularly inspecting and evaluating London's progress. "They have to take care of their athletes so it's important the time between venue and village is not too long and that there is somewhere close where athletes can stay during competition and not have to go back to the village."

The solution, which will avoid the need to build a temporary venue at Greenwich Peninsula, and save at least £20m, will see athletes offered the option of staying in hotels near Wembley for the duration of their competition or travelling around the North Circular ring road on a daily basis. Locog insists that the journey will only take around 45 minutes.

Although London made much of the fact that a high percentage of athletes would be housed in the Olympic Village during its bid, Oswald said the "exceptional" circumstances of the global economic slump made the decision the right one. London's mayor Boris Johnson, among others, has been pushing for money to be saved on temporary venues.

As the Olympic Stadium was included in London's bid to host matches in the 2018 World Cup, alongside Wembley, the new White Hart Lane stadium and the Emirates, Locog chairman Lord Coe said that its future as an athletics stadium was secure. 2018 chief executive Andy Anson said that a maximum of three London stadiums would eventually be included in the bid book.

One option, added Coe, might be for the stadium to remain at a capacity of more than 40,000 in order to facilitate a bid for the 2015 athletics World Championships.

The Olympic Park Legacy Company, which recently took over responsibility for the fate of the park after the games, will deliver its study on the future of the stadium next year. There is a fierce debate about whether it should remain at a capacity of 80,000 or 55,000 so that it can be used for future major event, or be reduced to around 28,000 as originally planned.